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A258064 Number of hands of n points in Spanish dominoes. 0
3, 9, 29, 67, 147, 283, 526, 893, 1470, 2287, 3451, 4990, 7030, 9559, 12697, 16375, 20664, 25406, 30621, 36034, 41618, 47022, 52174, 56696, 60548, 63362, 65186, 65746, 65186, 63362, 60548, 56696, 52174, 47022, 41618, 36034, 30621, 25406, 20664, 16375, 12697, 9559, 7030, 4990, 3451, 2287, 1470, 893, 526, 283, 147, 67, 29, 9, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

15,1

COMMENTS

In Spanish dominoes (double sixes) each of the four players gets a hand of seven stones. a(n) represents the number of possible different hands of n points. The lowest possible number of points in a hand is 15: (0-0 / 0-1 / 1-1 / 0-2 / 1-2 / 0-3) and one of the following stones: (2-2 / 1-3 / 0-4) which is three different combinations.

The highest hand is 69 points (6-6 / 6-5 / 5-5 / 6-4 / 5-4 / 6-3) and any of: (4-4 / 5-3 / 6-2). The sequence is finite and symmetrical around the peak: a(42) = 65746.

The sum of a(15) through a(69) is C(28,7) = 1184040.

LINKS

Table of n, a(n) for n=15..69.

Wikipedia, Dominoes, Tiles and suits

FORMULA

a(42+n) = a(42-n).

EXAMPLE

a(15)=3 since there are only 3 combinations of 7 stones that yield a hand of 15 points.

MATHEMATICA

Last /@ Tally[ Sort[ Total /@ Flatten /@ Subsets[ Flatten[ Table[{i, j} - 1, {i, 7}, {j, i}], 1], {7}]]] (* Giovanni Resta, Jun 23 2015 *)

CROSSREFS

Sequence in context: A047137 A058145 A218915 * A161590 A192245 A242558

Adjacent sequences:  A258061 A258062 A258063 * A258065 A258066 A258067

KEYWORD

full,fini,nonn

AUTHOR

Sergio Pimentel, May 18 2015

STATUS

approved

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Last modified April 3 15:16 EDT 2020. Contains 333197 sequences. (Running on oeis4.)